GA topology optimization using random keys for tree encoding of structures

Topology optimization consists in finding the spatial distribution of a given total volume of material for the resulting structure to have some optimal property, for instance, maximization of structural stiffness or maximization of the fundamental eigenfrequency. In this paper a Genetic Algorithm (GA) employing a representation method based on trees is developed to generate initial feasible individuals that remain feasible upon crossover and mutation and as such do not require any repairing operator to ensure feasibility. Several application examples are studied involving the topology optimization of structures where the objective functions is the maximization of the stiffness and the maximization of the first and the second eigenfrequencies of a plate, all cases having a prescribed material volume constraint.

[1]  J. Baldwin.  A New Factor in Evolution , 1896, The American Naturalist.

[2]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[3]  Edward L. Wilson,et al.  Incompatible Displacement Models , 1973 .

[4]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[5]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[6]  N. Kikuchi,et al.  Solutions to shape and topology eigenvalue optimization problems using a homogenization method , 1992 .

[7]  Martin P. Bendsøe,et al.  Topology design of structures , 1993 .

[8]  Prabhat Hajela,et al.  Genetic Algorithms in Structural Topology Optimization , 1993 .

[9]  Charles C. Palmer,et al.  Representing trees in genetic algorithms , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[10]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[11]  N. Kikuchi,et al.  Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method , 1994 .

[12]  N. Kikuchi,et al.  Topological design for vibrating structures , 1995 .

[13]  Roger L. Wainwright,et al.  Determinant Factorization: A New Encoding Scheme for Spanning Trees Applied to the Probabilistic Minimum Spanning Tree Problem , 1995, ICGA.

[14]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[15]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[16]  Random keys genetic algorithm with adaptive penalty function for optimization of constrained facility layout problems , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[17]  J. Gross,et al.  Graph Theory and Its Applications , 1998 .

[18]  N. Olhoff,et al.  Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives , 1999 .

[19]  N. L. Pedersen.  Maximization of eigenvalues using topology optimization , 2000 .

[20]  G. Rozvany.  Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics , 2001 .

[21]  Franz Rothlauf,et al.  Network Random KeysA Tree Representation Scheme for Genetic and Evolutionary Algorithms , 2002, Evolutionary Computation.

[22]  J. F. Aguilar Madeira,et al.  Multi-objective optimization of structures topology by genetic algorithms , 2005, Adv. Eng. Softw..

[23]  H. Rodrigues,et al.  Multiobjective topology optimization of structures using genetic algorithms with chromosome repairing , 2006 .

[24]  M. Y. Wang,et al.  An enhanced genetic algorithm for structural topology optimization , 2006 .

[25]  N. Olhoff,et al.  Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps , 2007 .